Fluid simulation does not follow animation
I found a way how you can solve this in a "relative" quickly way.  

Add a plane to your scene, subdivide length in 2 then subdivide it 10 times or so. Then Shrink wrap this plane, on your animated object.

Remove the fluidsim obstacle from your animated mesh.

For the Shrink wrapped plane, Add fluidsim (trough add modifiers!!!)
Then you get a non specific fuidsim control below it, it has a small properties icon, click it, set it to Fluid obstacle and animated mesh.

Below i add this working solution, note that I tuned the plane a bit.
Because shrink wrap had to fit in both open and close position.
Therefore i bended it, also I added another plane width fluid collision against leaking at the bottom.

Here is my final solution for this problem... btw it was a nice puzzle !!!



The only thing left todo is give those planes invisible materials, so you wont see them in final render.